If every one truly believed that what affects others is actually affecting themselves, I couldn't describe the all of benefits. One is a massive reduction of wars, violence and suffering.
It is a process though. I get angry, upset and do, on occasion, cause suffering in response to those emotions. What I am able to do is realise that I can observe this emotions as I do the universe, as it's all the same. By disconnecting from thoughts and emotions and observing them, they have much less effect. I can then use my thoughts as tool to analyse the situation and choose the appropriate path that will lead to a peaceful, beneficial resolution for me and others.
This does not happen every time, I still fall and slip. With repeated application, it will become a solid habit.
It's obvious and 'trivial' that negatively responding to negative emotional states will produce a negative outcome for myself, increasing my own suffering. This obvious fact fits within my insights, which is most important to me.